Gauge protection in non-abelian lattice gauge theories. (1st March 2022)

• Record Type: Journal Article
• Authors: Halimeh, Jad C; Lang, Haifeng; Hauke, Philipp
• Is Part Of: New journal of physics. Volume 24:Number 3(2022)
• Publication Date: 2022-03-01
• Subjects: lattice gauge theories -- gauge protection -- non-abelian gauge theories -- exact diagonalization; Physics -- Periodicals; Physics; Periodicals; 530.05
• DOI: 10.1088/1367-2630/ac5564
• Languages: English
• ISSNs: 1367-2630

Abstract

Abstract: Protection of gauge invariance in experimental realizations of lattice gauge theories based on energy-penalty schemes has recently stimulated impressive efforts both theoretically and in setups of quantum synthetic matter. A major challenge is the reliability of such schemes in non-abelian gauge theories where local conservation laws do not commute. Here, we show through exact diagonalization (ED) that non-abelian gauge invariance can be reliably controlled using gauge-protection terms that energetically stabilize the target gauge sector in Hilbert space, suppressing gauge violations due to unitary gauge-breaking errors. We present analytic arguments that predict a volume-independent protection strength V, which when sufficiently large leads to the emergence of an adjusted gauge theory with the same local gauge symmetry up to least a timescale ∝ V / V 0 3 . Thereafter, a renormalized gauge theory dominates up to a timescale ∝exp( V / V 0 )/ V 0 with V 0 a volume-independent energy factor, similar to the case of faulty abelian gauge theories. Moreover, we show for certain experimentally relevant errors that single-body protection terms robustly suppress gauge violations up to all accessible evolution times in ED, and demonstrate that the adjusted gauge theory emerges in this case as well. These single-body protection terms can be readily implemented with fewer engineering requirements than the ideal gauge theory itself in current ultracold-atom setups and noisy intermediate-scale quantum (NISQ) devices.